Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 35

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If $g_{1}, g_{2}, g_{3}$ are three geometric means between two positive numbers $a$ and $b$ , then $g_{1} g_{3}$ is equal to -

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Important Questions on Sequences and Series

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 36

If

x, y, z

are three geometric means between

6

and

54

, then

z

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 37

If three distinct numbers

a, b, c

are in

A . P .

and

b - a, c - b, a

are in

G . P .

, then

a : b : c

is equal to -

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 39

Let

a_{n}

be the

n th

term of a

GP

of positive numbers. If

\sum_{n = 1}^{100} a_{2 n} = α

and

\sum_{n = 1}^{100} a_{2 n - 1} = β

, such that

α \neq β

then the common ratio is

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 40

The series

\frac{2 x}{x + 3} + {(\frac{2 x}{x + 3})}^{2} + {(\frac{2 x}{x + 3})}^{3} + \dots \dots \infty

will have a definite sum when -

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 41

Four geometric means are inserted between the numbers

2^{11} - 1

and

2^{11} + 1

The product of these geometric means is

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 42

The value of

x

in

(- π, π)

which satisfies the equation

8^{1 + |\cos x| + | \cos^{2} x | + | \cos^{3} x ∣ + \dots \dots \infty} = 4^{3}

is -

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 43

If

a, b, c

are three distinct real numbers and they are in a

G . P .

If

a + b + c = x b

, then -

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 44

The product

2^{1 / 4} \cdot 4^{1 / 8} \cdot 8^{1 / 16} \dots

to

\infty

equal to -